Lake surface cooling drives littoral-pelagic exchange of dissolved gases

The extent of littoral influence on lake gas dynamics remains debated in the aquatic science community due to the lack of direct quantification of lateral gas transport. The prevalent assumption of diffusive horizontal transport in gas budgets fails to explain anomalies observed in pelagic gas concentrations. Here, we demonstrate through high-frequency measurements in a eutrophic lake that daily convective horizontal circulation generates littoral-pelagic advective gas fluxes one order of magnitude larger than typical horizontal fluxes used in gas budgets. These lateral fluxes are sufficient to redistribute gases at the basin-scale and generate concentration anomalies reported in other lakes. Our observations also contrast the hypothesis of pure, nocturnal littoral-to-pelagic exchange by showing that convective circulation transports gases such as oxygen and methane toward both the pelagic and littoral zones during the daytime. This study challenges the traditional pelagic-centered models of aquatic systems by showing that convective circulation represents a fundamental lateral transport mechanism to be integrated into gas budgets.


Supplementary Text
Estimation of oxygen consumption during lateral transport According to the potential oxygen consumption rate of  , 2 = 30 μmol O2 L -1 d -1 in Rotsee (46), the amount of oxygen consumed during the six-hour travel time  from the littoral (M1) to the pelagic region (MI) (Fig. 2A) amounts to  , 2 ⋅  = 9 μmol L -1 .This estimate represents ∼ 60 % of the lateral oxygen concentration difference of 14 μmol L -1 between sampling sites M1 and MI (Fig. 3A) and suggests an oxygen increase of ∼ 5 μmol L -1 at the base of the mixed layer which is consistent with our observations (Fig. 3D).If we assume first-order kinetics for the oxygen consumption,  , 2 =   2   2 where   2 ≈ 150 µmol L -1 is the oxygen concentration and   2 =  , 2 /  2 ≈ 0.2 d -1 is a decay rate.The advective Damköhler number relating the advection timescale to the reaction timescale   2 =   2 / (4, 7) is on the order of   2 ≈ 0.1 < 1 at length scales of  ≈ 1000 m and with the velocity of the convective circulation  ≈ 0.01 m s -1 .This estimate confirms that advective transport overcomes oxygen consumption (7).

Estimation of methane losses during lateral transport
The amount of methane oxidized during the eight-hour travel time  from the pelagic region to MT (300 m distance travelled at 0.01 m s -1 velocity) is  ⋅  , 4 ≈ 2 μmol L -1 according to typical oxidation rates of  , 4 = 5 μmol CH4 L -1 d -1 in autumn in Rotsee (18,41).Atmospheric exchange additionally decreased the methane concentration by  ⋅   / ≈ 0.5 μmol L -1 , with   ≈ 0.1 μmol CH4 m -2 s -1 the atmospheric methane flux in Rotsee estimated from meteorological data (fig.S7) and measured in autumn (40), and  = 7 m the average lake depth between MT and the pelagic region.Based on the initial concentration difference of 6 μmol L -1 between MT and MI (Fig. 4A), the total methane loss of ∼ 3 μmol L -1 suggests an increase of surface methane concentration of ∼ 3 μmol L -1 at MT, which agrees well with the observed  4 (Fig. 4C).The advective Damköhler number is given by   4 =   4 / (4, 7), where  ≈ 0.01 m s -1 is the velocity of the convective circulation,   4 = ( , 4 +   /)/  4 ≈ 0.5 d -1 is the methane decay rate and   4 ≈ 13 μmol L -1 is the methane concentration offshore.The Damköhler number is   4 ≈ 0.5 < 1 at length scales of  ≈ 1000 m, which confirms that advective transport overcomes methane consumption.

Contribution of convective circulation to pelagic methane peaks
In Lake Hallwil and Lake Stechlin, where methane peaks of  4 ≈ 0.1 − 1 μmol L -1 in the oxic layer have been reported at a distance of  ∼ 1 km from the shore, methane oxidation rates and littoral-pelagic concentration differences were  , 4 ≈ 0.01 μmol CH4 L -1 d -1 and    4 ≈ 0.1 − 1 μmol L -1 (gradient of |   4 /| ≈ 10 −1 − 10 0 μmol L -1 km -1 ), respectively (8,10,13).According to our estimates from Rotsee (velocity of the lower circulation limb   ≈ 0.01 m s -1 ), we expect convective circulation to generate a peak of  4 =    4 −  , 4 /  ≈ 0.1 − 1 μmol L -1 , if vertical mixing between the two limbs is neglected.This estimate agrees with the orders of magnitude of reported  4 , indicating that convective circulation is at least as important as other chemicophysical processes generating methane peaks.1, B and C) with the gas experiment period on 24-26 November scaled in bold on the x-axis of each plot.(A) The non-penetrative surface buoyancy flux (B0), the shortwave surface buoyancy flux (BSW,0) and the net surface buoyancy flux ( 0, =  0 +  ,0 ) were computed as  0 =  ,0 / , and  ,0 =  ,0 / , where  ,0 is the sum of sensible heat, latent heat and longwave radiation fluxes,  ,0 is the incoming shortwave radiation corrected for the wavelengths range of the pyranometer and for the water surface albedo,  is the thermal expansivity,  is the gravitational acceleration,  is the water density and  , is the specific heat capacity of water.Each heat flux component was calculated following

Fig. S1 .
Fig. S1.Bathymetric map of Rotsee.Red and orange dots indicate the location of the seven measurement stations.Continuous measurements of dissolved gases were collected at M0 and MT (purple dots).The green star depicts the weather station.Blue arrows show the small inflow and the outflow.Black lines with white depth labels are 2 m spaced isobaths.

Fig. S2 .
Fig. S2.Forcing conditions and convective circulation.Six-day time series of surface buoyancy fluxes and air-water temperature differences (A), wind speed and direction at 3 m height (B), dimensionless Monin-Obukhov length (C), lateral temperature gradients between M1 and MI (D), cross-shore velocity at M1 (E) and water temperature at MB (F), on 21-27 November 2020 (same period as in Fig.1, B and C) with the gas experiment period on 24-26 November scaled in bold on the x-axis of each plot.(A) The non-penetrative surface buoyancy flux (B0), the shortwave surface buoyancy flux (BSW,0) and the net surface buoyancy flux ( 0, =  0 +  ,0 ) were computed as  0 =  ,0 / , and  ,0 =  ,0 / , where  ,0 is the sum of sensible heat, latent heat and longwave radiation fluxes,  ,0 is the incoming shortwave radiation corrected for the Fink et al. (2014) (47) except the incoming longwave radiation directly measured at the Lucerne weather station, 4 km from Rotsee, as inDoda et al. (2022) (29).Destabilizing fluxes are positive (cooling), whereas stabilizing fluxes are negative (heating).Net surface cooling ( 0, > 0) occurred over the entire experiment period(24)(25)(26).The grey dotted line corresponds to the air-water temperature difference   −   .(B) The black line and the green dots show the 10 min wind speed and direction, respectively.(C) The two horizontal dashed lines indicate the windconvection interaction regime 0.1 ≤   ≤ 0.5(36).(D) The lateral temperature gradients were calculated from mixed layer averaged temperature at M1 and MI (390 m apart).Positive temperature gradients correspond to differential cooling.(E) The cross-shore velocity is represented as in Fig.1, B and C. (F) The red line depicts the mixed layer depth, defined as in Doda et al. (2022)(29).The daily thickening of the stratified bottom layer in the afternoon (rise of the red interface) indicates intrusions of cold water from convective circulation.Black lines in (E-F) are 0.1°C spaced isotherms, from linearly interpolated temperature between each thermistor (black ticks on the right y-axis).

Fig. S3 .
Fig. S3.Forcing conditions and temperature time series at each mooring.Six-day time series on 21-27 November 2020 (same period as in Fig. 1, B and C) with the gas experiment period on 24-26 November scaled in bold on the x-axis of each plot.(A) Net surface buoyancy flux (black line) and wind speed along the x-axis (green line).(B to F) Temperature time series at each sensor depth at M1 (B), MT (C), M2 (D), MI (E) and MB (F).The red dotted circles indicate a stratified layer at the base of the mixed layer associated with convective circulation.

Fig. S4 .
Fig. S4.Cross-shore variability of temperature and oxygen saturation.Temporally averaged profiles of temperature (A) and oxygen saturation (B) at five locations along the cross-shore transect (25 November, 03:00-20:00).Shaded areas depict the standard deviation.(A) The lateral mixed layer temperature gradient due to differential cooling between M1 and MI (littoral region) is / ≈ 0.4 °C km -1 .The bottom stratification induced by the downslope gravity current is visible at M1, MT and M2.The intrusion at MI creates a cold layer at the base of the mixed layer that is not observed in the temporally averaged profile at MB. (B) The lateral mixed layer oxygen gradient between M1 and MI (littoral region) of  2 / ≈ −10 % km -1 is the same as in fig.S5A.The downslope oxygen transport increases the oxygen concentration near the bottom at M1, MT and M2.The intrusion at MI creates an oxic peak at the base of the mixed layer that is not observed at MB.

Fig. S5 .
Fig. S5.Oxygen transport by the lower circulation limb expressed in oxygen saturation.Same figure as Fig. 3 with percentage of oxygen saturation instead of oxygen concentration.

Fig. S6 .
Fig. S6.Surface transport of methane across the littoral region.(A) Time series of depthaveraged cross-shore velocity in the lower limb (purple, Ulow > 0) and in the upper limb (green, Uup < 0) of the circulation at MT, and in the lower limb at M1 (dotted line, Ulow > 0), from 24 to 26 November.Shaded areas depict the standard deviation.(B) Time series of methane concentration in the upper limb of the circulation at MT (solid line) and M0 (dotted line).Shaded areas depict the standard deviation between five samples.The vertical dashed lines show two flow intensification events in the littoral region on 25 November, after 07:00 and after 23:00.Both events enhanced the surface methane transport from MT to M0, as shown by the sharp concentration increase at M0 4-5 h after each flow intensification.

Fig. S8 .
Fig. S8.Littoral and pelagic surface methane concentrations in summer (July 2019).Surface (1-2 m depth) methane concentrations were measured from water samples with the headspace method(18).The error bars indicate the standard deviation between replicates.Littoral methane concentrations were constantly higher than pelagic concentrations, leading to a negative lateral methane gradient of  4 / ≈ −10 −1 μmol L -1 km -1 between M0 and MB.

Fig. S9 .
Fig. S9.Scaling approach assessing the contribution of lateral advection, horizontal turbulent diffusion and reaction to the mass balance of a dissolved substance.Each of the three dimensionless numbers compares the importance of two processes: the Péclet number Pe, advective Damköhler number Daadv and dispersive Damköhler number Dadisp relate advection to turbulent diffusion, reaction to advection and reaction to turbulent diffusion, respectively.Parameter values specific to this study are shown (see supplementary text), where the characteristic length scale is between 100 and 1000 m, lateral advection is driven by convective circulation (CC) and dissolved constituents are oxygen (blue) and methane (red).In this example, lateral advection dominates the mass balance by exceeding fluxes associated with horizontal turbulent diffusion and reactions.In contrast, horizontal turbulent diffusion is not fast enough to overcome reaction rates.

Fig. S10 .
Fig. S10.Cross-shore velocity scaling of convective circulation.Daily averaged cross-shore velocity as a function of the velocity scale for 85 days with convective circulation between July 2019 and January 2020 (colored dots) and during the gas experiment (black cross).The black line is the linear fit  = 0.33( 0   ) 1/3 , where  0 is the non-penetrative surface buoyancy flux (see fig.S2) and   is the width of the mixed region shallower than the mixed layer depth, both averaged during the cooling period.This figure is the same as Fig. 6a in Doda et al. (2022) (29) with the additional data from the gas experiment.

Table S1 .
Characteristics of the measurement stations.